TRAFFIC congestion has caused huge loss to society and. A Grouping Based Cooperative Driving Strategy for CAVs Merging Problems

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1 1 Grouping ased ooperative riving Strategy for Vs Merging Problems Huile Xu, Shuo Feng, Yi Zhang, Member, IEEE, and Li Li, Fellow, IEEE arxiv: v1 [cs.sy] 4 pr 2018 bstract In general, there are two kinds of cooperative driving strategies, planning based strategy and ad hoc negotiation based strategy, for connected and automated vehicles (Vs) merging problems. The planning based strategy aims to find the global optimal passing order, but it is -consuming when the number of considered vehicles is large. In contrast, the ad hoc negotiation based strategy runs fast, but it always finds a local optimal solution. In this paper, we propose a grouping based cooperative driving strategy to make a good tradeoff between consumption and coordination performance. The key idea is to fix the passing orders for some vehicles whose intervehicle headways are small enough (e.g., smaller than the preselected grouping threshold). From the viewpoint of optimization, this method reduces the size of the solution space. brief analysis shows that the sub-optimal passing order found by the grouping based strategy has a high probability to be close to the global optimal passing order, if the grouping threshold is appropriately chosen. series of simulation experiments are carried out to validate that the proposed strategy can yield a satisfied coordination performance with less consumption and is promising to be used in practice. Index Terms onnected and utomated Vehicles (V), cooperative driving, merging problem, grouping based strategy. I. INTROUTION TRFFI congestion has caused huge loss to society and aroused wide concern in recent years[1], [2]. Researchers had found that orderless merging at on-ramps is one of the main causes of traffic congestion and needs to be carefully handled [3]. The emergence of onnected and utomated Vehicles (Vs) provides a promising way for solving merging problems. With the aid of vehicle-to-vehicle (V2V) and vehicleto-infrastructure (V2I) communication, Vs can obtain real operational data of adjacent vehicles and receive control actions[4], [5], [6]. It has become a common vision that Vs will increasingly appear on the road in the near future and help to alleviate traffic congestion[7], [8]. Manuscript received in pril 5, 2018; This work was supported in part by National Natural Science Foundation of hina under Grant and eijing Municipal Science and Technology ommittee Project under Grants and Z179074Z. (orresponding author is Li Li). H. Xu is with epartment of utomation, Tsinghua University, eijing , hina. ( hl-xu16@mails.tsinghua.edu.cn) S. Feng is with epartment of utomation, Tsinghua University, eijing , hina. ( s-feng14@mails.tsinghua.edu.cn) Y. Zhang is with epartment of utomation, NRist, Tsinghua University, eijing , hina and also with the Tsinghua-erkeley Shenzhen Institute (TSI), Tower 2, Nanshan Intelligence Park 1001, Xueyuan lvd., Nanshan istrict, Shenzhen , hina. ( zhyi@tsinghua.edu.cn) L. Li is with epartment of utomation, NRist, Tsinghua University, eijing , hina. (Tel: +86(10) , li-li@tsinghua.edu.cn). long with the development of Vs, researchers became interested in finding an efficient cooperative driving method for Vs merging problems. It is pointed out in [9] and [10] that the key to the merging problem is to determine the optimal passing order. s summarized in [4], [11], there are two kinds of cooperative driving strategies, planning based strategy and ad hoc negotiation based strategy, for determining the passing order. Planning based strategy: The planning based strategy considers Vs within a certain scope of the merging zone and provides long-term scheduled control actions for Vs. It tries to enumerate all possible passing orders to find the global optimal solution. Most state-of-the-art studies transfer the merging problem into various optimization problems [12], [13], [14], [15], [16], such as mixed integer linear programming (MILP), receding horizon control (RH). However, the consumption for solving the problem increases sharply as the number of vehicle increases, which makes these methods difficult to be applied in practice. d hoc negotiation based strategy: d hoc negotiation based strategy considers Vs that are about to arrive at the merging zone and formulate short-term scheduled control actions via bilateral negotiations. It uses greedy search algorithms to determine the passing order and always lead the passing order to be roughly first-in-first-out (FIFO)[17], [18]. This strategy has a fast online implementation[19], [20]. However, they cannot guarantee that the passing order is global or good enough [11], [21], [22]. To overcome the above limitations, we propose a grouping based cooperative driving strategy for Vs merging problems. The key idea of grouping is to consider some vehicles (whose inter-vehicle headways are small enough) as a whole in planning. This will narrow down the size of solution space and thus save planning. The idea of grouping had been initialized in [9], [10] for faster V2X communications. Now, we apply the same trick for planning of cooperative driving. First, Vs within a control zone will be self-organized into several groups by a grouping method. Generally, if the headway between two consecutive Vs is smaller than a grouping threshold, then they will be grouped into the same group. n adaptive grouping threshold is designed to control the size of groups. The maximum number of groups is fixed to limit the maximum consumption. Second, the passing order of Vs in the same group is consecutively fixed. Therefore, the number of possible passing orders is largely reduced. Planning in such a reduced solution space will lead to a sub-optimal solution. brief analysis shows that the sub-optimal passing order

2 2 TLE I: Nomenclature and representative values Symbol Meaning Value The symbols below are treated as constants t 1 The minimum safety gap between two Vs on the same movement 1.5s t 2 The minimum safety gap between two Vs on the conflict movements 2s a max,a min The maximum and minimum acceleration -3m/s 2, 3m/s 2 v max,v min The maximum and minimum velocity 10m/s, 0m/s The symbols below are treated as variables δ Grouping threshold x i (t) The location of V i at t v i (t) The velocity of V i at t a i (t) The acceleration of V i at t t min,i The minimum access of V i t assign,i The assigned access of V i The symbols below are treated as functions or sets J Objective function Search space S Selected set G Good enough set found by the grouping based strategy has a high probability to be close to the global optimal passing order, if the grouping threshold is appropriately chosen. To validate this finding, some simulation experiments are carried out. Results indicate that the proposed strategy for merging problems can yield a good enough passing order with little consumption. To give a better presentation of our findings, the remaining of this paper is arranged as follows. Section II formulates the merging problem at highway on-ramps. Section III presents three cooperative driving strategies. Section IV gives a brief analysis of the grouping based strategy. Section V provides the simulation results of several experiments to validate the effectiveness of the proposed strategy. Finally, concluding remarks are given in Section VI. II. PROLEM FORMULTION also can be employed with slight modification[9], [10]. Tab.I gives the nomenclature list of the major symbols used in this paper. ooperative driving strategy aims to schedule the velocity and acceleration profiles of all Vs [19], [23]. s pointed out in [11], the performance of a strategy mainly depends on the passing order of vehicles and the differences between different motion planning methods are negligible. Thus, the merging problem is transferred into an optimization problem with respect to the passing order together with a simple motion planning method which requires little computational cost. In this paper, we will focus on the first problem. The details of the motion planning used in this paper are presented in ppendix. Lane 1 6 Group 2 ontrol Zone Length L = 300m Group 1 Merging Zone 20m Once a V enters into the control zone, it is given a unique identity. V i means it is the ith V that enters into the control zone. The movements of each vehicle within the control zone may be re-scheduled for every T minutes. Every the schedule begins, the objective of the optimization problem can be written as Fig. 1: typical merging scenario at a highway on-ramp. This paper considers a highway on-ramp with a single lane in each movement as shown in Fig.1. The shadow area is called as merging zone where two Vs on different movements may collide. L is the distance from the entry of control zone to the merging zone. Usually, L is about 50m-200m. The multiple lane merging scenario is similar and the proposed strategy J = ω 1 max(t assign,i ) + ω 2 n i=1(t assign,i t min,i ), (1) where t assign,i is the decision variable and represents the desired access to the merging zone for V i. n is the total number of vehicles in the control zone. t min,i is the minimum access

3 3 to the merging zone and can be easily derived by t min = t 0 +t 1 +t 2, (2a) v = v a maxx 0, (2b) ( vmax v 0 t 1 = min, v v ) 0, (2c) a max a max ( 2amax x 0 v 2 max + v 2 ) 0 t 2 = max,0, (2d) 2a max v max where x 0 is initial location, v 0 is initial velocity, and t 0 is the when the V enters into to the control zone. The first term in the objective is to minimize passing and the second term is to decrease the delay of Vs. ω 1 and ω 2 are weighted parameters of the objective. Suppose that V i and V i+1 are two consecutive Vs on the same movement. To avoid a rear-end collision, we require that the minimum allowable safety gap between them is larger than t 1 t assign,i t assign,i+1 t 1. (3) Suppose that V i and V j are two Vs on conflict movements. To avoid a lateral collision, we require the minimum allowable safety gap between them is larger than t 2 t assign,i t assign, j t 2, OR t assign, j t assign,i t 2. The constraints ensure that for any two Vs i and j that are on the conflict movements, only one V can enter into the merging zone after the other V has left the merging zone. Moreover, we assume that t 2 is greater than t 1. Introducing some binary variables, we can formulate the whole optimization problem in terms of the passing order (decision variable) b = [b k1,l 1,,b k,l,,b kn1,l n2 ] {0,1} n 1 n 2 as below min t assign,b (4) ω 1 max(t assign,i ) + ω 2 n i=1(t assign,i t min,i ) (5a) subject to a min a i a max v min v i v max t assign,i t assign, j t 1 t assign,k t assign,l + M b k,l t 2 t assign,l t assign,k + M (1 b k,l ) t 2 k N 1 = {k 1,k 2,,k n1 } l N 2 = {l 1,l 2,,l n2 } b k,l {0,1} (5b) (5c) (5d) (5e) (5f) (5g) (5h) (5i) where M is a sufficiently big number, N 1 and N 2 are two sets that contain all Vs travelling on two movements. The sizes of N 1 and N 2 are n 1 and n 2 respectively. b k,l is a binary number. When b k,l equals 0, V k passes through the merging zone earlier than V l. Similar to [9], the passing order also can be denoted as a string, which is more intuitive in the analysis. For example, string means V, V, V and V enter the merging zone sequentially. Each such a string corresponds to a possible value of b. If the passing order is given, the problem (5) can be solved by a simple iteration algorithm shown in lgorithm 1. lgorithm 1 Simple Iteration lgorithm Input: passing order P Output: n objective value J and t assign 1: t assign (1) = V P,1 [t min ] 2: for each i [2,length(P)] do 3: if V P,i 1 and V P,i are on the same movement then 4: t assign (i) = max(t assign (i 1) + t 1,V P,i [t min ]) 5: else 6: t assign (i) = max(t assign (i 1) + t 2,V P,i [t min ]) 7: end if 8: end for 9: J = ω 1 max(t assign ) + ω 2 length(p) i=1 (t assign (i) V P,i [t min ]) Here, V[t min ] means the minimum access t min of the V. V P,i is the ith V passing through the merging zone in the passing order P. Obviously, the complexity of the lgorithm 1 is O(n 1 + n 2 ). III. OOPERTIVE RIVING STRTEGIES In this section, we will present three cooperative driving strategies to solve the above optimization problem (5).. Planning ased Strategy Generally, planning based strategy directly attacks the above mixed integer linear programming (MILP) problem (5). We can use either tree-based enumeration method [10], [11] or classic branch-and-bound method to solve this MILP [24], [25] However, there are 2 n 1n 2 possible values for variable b. So, the complexity of branch-and-bound method is still exponential in the worst case. Numerical tests show that the enumeration based method only works well when the number of vehicles is less than 12 [11]. The efficiency of the branch-and-bound method is similar.. d Hoc Negotiation ased Strategy d hoc negotiation based strategy uses greedy search to solve Problem (5). s summarized in [17], [18], the passing order in many ad hoc negotiation methods follows the firstin-first-out (FIFO) principle. In other words, all Vs in the control zone estimate their arrival points to the merging zone if no schedule is given. The passing order is derived by sorting their arrival points in ascending order. When the passing order is determined, the degenerated problem is easily solved by lgorithm 1. It is easy to show that the complexity of ad hoc negotiation based strategy is O(n 1 + n 2 ).

4 4. Grouping ased Strategy Grouping based strategy can be viewed as a modification of planning based strategy. Its main idea is to search the sub-optimal passing order among a subset of search space instead of all passing orders. This subset is determined by the following grouping method: if the headway between two consecutive vehicles is smaller than a grouping threshold, then they will be grouped into the same group. The vehicles in a group are assumed to enter the merging zone consecutively without any other vehicles interruption. The grouping threshold determines the number of groups. To control the consumption, the maximum allowable number of groups is set as 12 in this paper. If the number of groups is larger than 12, the consumption will be too large for practical applications. Fortunately, we do not need to consider too many vehicles for merging problems. So, 12 groups usually meet our expectation to balance the complexity and efficiency of the planning algorithm. Moreover, we apply an adaptive threshold in this paper. The initial value of the threshold is set as 1.5m which is the minimum safety gap between two consecutive vehicles. If all vehicles had been grouped into less than 12 groups, we stop. Otherwise, we increase the threshold for 0.1s each and re-group the vehicle in an iteration manner, until the number of groups is not larger than 12. When grouping is done, we consider each group as a special V and calculate the optimal passing order for these special Vs. Finally, the obtained passing order for the groups of vehicles will be interpreted into the passing order for all vehicles. The major benefit of grouping is to reduce the complexity of the problem. If the maximum number of groups is c, the complexity of the grouping based strategy is approximately O(c! (n 1 +n 2 )). This greatly saves the planning, especially when (n 1 + n 2 ) is large. To better understand the benefit of the proposed strategy, we briefly introduce some typical cases for examples. s shown in Fig.1 as an example. 7 vehicles are grouped into 4 groups. s shown in Fig.2, the number of searched passing orders is largely reduced from 7! to 6. In the rest of this paper, we will show that the sub-optimal passing order found by the grouping based strategy has a high probability to be close to the global optimal passing order, if the grouping threshold is appropriately chosen. IV. RIEF NLYSIS In this section, we will show that it is usually unnecessary to divide two consecutive vehicles whose intervehicle headway is very small apart and let other vehicles cut in. More precisely, we study a very basic scenario in which we can enumerate all the candidate passing orders. We compare the traffic efficiency in each possible situation with and without grouping. We will show that the occurring probability for the special case (in which grouping leads to a larger passing than not grouping) is very small. To this end, let us consider the following scenario that consists of four Vs. V, V, and V are on lane 1; and V is on lane 2; see Fig.3. The headway between V and V is less than the grouping threshold, so they may be in a group. For convenience, we denote the initial headway between V i and V j as h i, j, when these vehicles enter the control zone. lso, we have the reciprocal relationship between the average headway and the arrival rate λ of vehicles. ll valid passing orders with and without grouping are shown in Fig.4. s aforementioned, we use a string to denote the passing order of vehicle for presentation simplicity. Lane 1 (a) Grouping ased Strategy: Fig. 3: merging scenario. Merging Zone Vehicle on the lane 1 Vehicle on the lane 2 (b) Enumeration ased Method: Passing order 1: Group 1 Group 2 Group 3 Group 4 (a) Grouping ased Strategy: (b) Permutation ased Method: Passing order 2: Group 1 Group 3 Group 2 Group Passing order 3: Group 1 Group 3 nnotation: Group 4 Group 2 Passing order 4: Passing order 5: Group 3 Group 1 Group 4 Group Passing order 6: means will pass through the MZ earlier than nnotation: 1 2 (a) Group-based permutation: n vehicles means V1 will pass through the MZ earlier than V2 Group 3 Group 4 Group 1 Group 2 Group 3 Group 1 Group 2 Group 4 Fig. 2: The possible passing orders for the grouping based (b) Permutation: strategy. n order of n-m groups vehicles corresponds to am passing vehicles order of Vs. Fig. 4: (a) ll 3 passing orders after grouping. (b) ll 4 passing orders without grouping. (a) Group-based permutation: n vehicles m 1 vehicles m 2 vehicles m k vehicles Obviously, for this scenario, if the global optimal solution (passing order) is,, or, grouping does not hinder us to find the global optimal solution. The only (b) Permutation: special case that we should take care is the global optimal n 1 vehicles m 1 vehicles n 2 vehicles m k vehicles solution is. In the rest, we will discuss when can be the global optimal solution. n k+1 vehicl (a) Group-based permutation: n vehicles k vehicles

5 5 The optimal solution is means that we have t t, t t and t t simultaneously. Let us take t t as an example to show what constraints are needed. If the passing order is, the assigned of each vehicle can be derived according to lgorithm 1. t assign, = t min,, t assign, = max{t assign, + t 2,t min, }, t assign, = max{t assign, + t 2,t min, }, t assign, = max{t assign, + t 1,t min, }. (6a) (6b) (6c) (6d) Then, the total passing of all 4 vehicles under the passing order is t =t assign, =max{t min, + t t 2,t min, + t 1, t min, + t 1 + t 2,t min, }. Similarly, the total passing of all 4 vehicles under the passing order is t =max{t min, + t t 2,t min, + 2 t 2, t min, + t 2,t min, }. For each case, we will compare the value of t and t. The following analysis shows that only in the fourth case, t can be smaller than t. 1) if t = t min, + t t 2, (7) (8) t t t min, + t t 2 t = 0. (9) 2) if t = t min, + t 2, t t t min, + t 1 + t 2 t = t 1. (10) 3) if t = t min,, t t t min, t = 0. (11) 4) if t = t min, + 2 t 2 and t > t min, + t 1 + t 2, t t < 0. (12) Therefore, the special case (e.g. t t < 0) only occurs when the following constraints are satisfied. t min, t min, + t 2 t 1 t min, + t 1 t min, (13) t min, t min, + 2 t 2 The constraints for t t and t t can be derived by the similar way. Summarizing all the constraints and relaxing some of them, we get t 1 h, δ t 1 + t 2 t min, t min, t 1 + t 2 + δ (14) t 1 + t 2 t min, t min, 2 t 2 + δ Finally, we discuss the relationship between t min, j t min,i and the headway h i, j to check the occurring probability of such a case. For simplicity, we assume that all Vs are operated at the maximum velocity and thus have t min, j t min,i = h i, j. s suggested in [5], we suppose that the headway h follows displaced exponential distribution as f (h) = 1 h τ e (h τ)/( h τ), h τ, (15) where h = 1/λ is the average headway, λ is the average arrival rate, τ is the minimum headway which equals t 1 in the paper. The cumulative distribution function of the headway is P(h H) = F(H) = 1 e (H t 1)/( h t 1 ). (16) For presentation convenience, we define F(H 1,H 2 ) = P(H 1 h H 2 ) = F(H 2 ) F(H 1 ). ccording to (16), the probability of satisfying the constraints (14) is P = F 1 ( t 1,δ) F 2 ( t 2 t 1, t 2 t 1 +δ) F 1 ( t 1 + t 2,2 t 2 +δ). (17) When we set t 1 = 1.5s, δ = 2s, t 2 = 2.5s, and λ 1 = λ 2 = 0.2veh/s, this probability is about 1.3%. That is, under this parameter setting, the probability that the sub-optimal solution of the grouping based strategy is worse than the global optimal solution is 1.3%. This is really a small chance. The above analysis reveals the major reason why the suboptimal solution of the grouping based strategy is good enough in most situations. However, this method becomes improbable to analyze the cases that consist of a lot of vehicles, since the number of possible cases increases exponentially. So, in the rest of this paper, we resort to numerical tests to further validate our conclusion. V. SIMULTION TESTS The first experiment introduce the concept of alignment probability initialized in ordinal optimization [26], [27], [28] as the measure to validate that the sub-optimal solution found by grouping method is a good enough solution. We also use the histogram of all possible solutions (passing orders) of the merging problem to show that the grouping based strategy obtains a good enough solution. The second experiment shows that the consumption of the grouping based strategy is much less than conventional planning based methods. Finally, the third experiment compares the performance of different cooperative driving strategies. In these experiments, the vehicles arrival at each movement is assumed to be a Poisson process. The arrival rate can be varied to test the performance of the proposed strategy under different traffic demands. The vehicles arrival rates at two movements are the same unless otherwise specified. The weight parameters of objective function ω 1 and ω 2 both are 0.5. The minimum safety gaps of three strategies are the same. The minimum safety gap between two Vs on the same movement is 1.5s, and the minimum safety gap between two Vs on the conflict movements is 2s. ll experiments are carried out on a MTL platform in a personal computer with an Intel i7 PU and an 8G RM.

6 verage consumption (s) lignment Probability Probability(%) 6. The Optimality of the Grouping ased Strategy The grouping based strategy can be regarded as a sampling technique to narrow down the search space and speeding the search process. lignment probability is a nice measure to characterize the degree of matching between the original solution space S and the sampled subset G [28]. Suppose G is a good enough set which consists of the top-g solutions of search space. g is the ranking index. For example, the top-1 solution denotes the best solution. S is a selected set where the members are selected by using certain sampling technique or selection rule. G S k means there are at least k truly good solutions in S. k is called the alignment level and P( G S k ) is called alignment probability[26], [27]. In this paper, the alignment probability is calculated through simulation experiments. In the experiment, we vary λ from 0.1 veh/(lane s) to 0.25 veh/(lane s). Under each certain arrival rate, we simulate a 20 minutes traffic process. We record all solutions of the enumeration based method, the estimated optimal solution of the grouping based strategy, consumption, and the number of vehicles in the merging zone. We compare the estimated optimal solution with top-g solutions to count the alignment probability. We set the alignment level k as 1, since we care about whether there is a good enough solution in the selected set. The alignment probabilities with respect to different numbers of vehicles are shown in Fig number of vehicles = 5 number of vehicles = 10 number of vehicles = 15 number of vehicles = 20 number of vehicles = g Fig. 5: lignment probability versus top-g solutions parameterized by the number of vehicles. It is clear that the sub-optimal solution always is among the top-0.025% solutions and is good enough. Even when the number of vehicles equals 20 and the average number of the possible solutions is about , the sub-optimal solution found by grouping method is among the top-32 solutions. In other words, from the viewpoint of solutions order, the sub-optimal solution can be very close to the global optimal solution with a high probability. For a special merging scenario, we can calculate all the objective values for all the possible solutions (passing orders) and plot them in a histogram manner. This histogram intuitively describes the performance of solutions. Fig.6 gives such a histogram for solution values for a merging scenario with 25 Vs. There are possible passing orders for the merging scenario Enumeration based method: Optimal solution = s Time consumption = s Grouping based strategy: Optimal solution = s Time consumption = 0.039s FIFO based method: Optimal solution = s Time consumption = 0.011s Objective function value(s) Fig. 6: The histogram of solution values for a merging scenario with 25 Vs. We apply the FIFO based ad hoc negotiation strategy and the grouping based strategy for the same scenario. Then, we mark the locations of their optimal solutions in the Fig.6. It is clear that the solution found by the grouping based strategy is nearly the same as the global optimal solution; while the solution found by the FIFO based ad hoc negotiation strategy is far away from the global optimal solution. Indeed, the solution found by the grouping based strategy is the 7th best solution; while the solution of the FIFO based strategy ranks th.. The Time onsumption of the Grouping ased Strategy To check the average consumption with respect to different numbers of vehicles that will be considered, we vary the vehicle arrival rate λ from 0.1 veh/(lane s) to 0.25 veh/(lane s). Under each certain arrival rate, we simulate a 20 minutes traffic process. We record corresponding consumption and the number of vehicles in the merging zone Planning based strategy Grouping based strategy Number of vehicles Fig. 7: semi-log plot of average consumption against the number of vehicles. The result comes from 4800 merging scenarios. s shown in Fig.7, the results indicate that the average consumption of the planning based strategy (enumeration based method) increases almost exponentially. lthough the

7 7 TLE II: omparison results of three cooperative strategies average arrival rate 1 strategies average delay(s) average consumption(ms) average number of Vs Grouping based Planning based d hoc negotiation based Grouping based Planning based d hoc negotiation based Grouping based Planning based d hoc negotiation based Grouping based Planning based d hoc negotiation based Grouping based Planning based d hoc negotiation based Suppose average arrival rates on two movements are the same. 2 When the arrival rates on two movements are 0.3, the traffic becomes seriously congested and most Vs block in the upstream after 5-minute simulation. Thus, the results in this parameter setting are the results of a 5-minute simulation. planning based strategy gives the global optimal solution, it is difficult to be applied in practice. In contrast, since we restrict the maximum group number is 12, the average consumption of the grouping based strategy reaches a saturated value, when the number of vehicles is larger than 15. ombining Fig.5 and Fig.7, we can conclude that the grouping method can find a good enough solution within a short enough.. omparison of ifferent ooperative riving Strategies with Respect to rrival Flow Rate To compare the performance of different cooperative driving strategies, we calculate the delay of V i as t delay,i = t assign,i t min,i. (18) and the consumption that a strategy takes to find the passing order. less delay indicates that a better performance; and a less consumption indicates that a faster speed. In the simulation, the initial merging scenario contains five Vs whose initial positions are generated randomly. The average arrival rate λ of the following Vs can vary from 0.1 veh/(lane s) to 0.3 veh/(lane s). For each arrival rate, we simulate a 20 minutes traffic process. Grouping based strategy, planning based strategy (branch and bound method), and ad hoc negotiation based strategy (FIFO based method) are respectively applied to the same initial merging scenario. ll the considered Vs trajectories are replanned every T = 2 seconds. In planning based strategy, the MILP problem (5) is directly solved by VX software with Mosek solver. The Mosek solver makes use of branch and bound method to handle integer variables [24]. The performance measures are shown in Tab.II. s shown in Tab.II, the average delay of the grouping based strategy and planning based strategy is similar and the biggest difference is only 0.04 s/veh. However, the consumption of the planning based strategy increases sharply with the arrival rate. When the arrival rate equals 0.3, the average consumption of the planning based strategy is more than 11 seconds. t the same, the calculation of the proposed strategy always can be finished within 40 ms. On the other hand, under the situation of high arrival rate, the coordination performance of the ad hoc negotiation based strategy is extremely bad. When the arrival rate equals 0.25, the average delay of the ad hoc negotiation based strategy is more than twice that of other two strategies. lthough the ad hoc negotiation based strategy is -saving, its performance is far from satisfactory. It is obvious that the grouping based strategy makes a good tradeoff between the planning based strategy and ad hoc negotiation based strategy. Its good traffic control performance and short consumption make it practical for real applications. VI. ONLUSION In this paper, we propose a grouping based strategy to make a good tradeoff between computation complexity and traffic control efficiency. Its key idea is to narrow down the number of candidate passing orders and search a suboptimal passing order among a subset of the solution space. nalysis and simulation results validate that the sub-optimal solution found by the grouping based strategy has a high probability to be close to the global optimal solution, no matter what vehicle arrival rate is given. eing compared with the planning based strategy, the grouping based strategy yields similar traffic efficiency with much less calculation. eing compared with ad hoc negotiation based strategy, the grouping based strategy gives much better traffic efficiency with similar calculation. Thus, we recommend the grouping based strategy as a promising cooperative driving strategy in practice. It should be pointed out that the empirical dynamic constraints of vehicles are not considered in this paper. We are

8 velocity velocity velocity velocity velocity 8 currently building several automated vehicle prototypes. In the near future, we will test our grouping based strategy in a real on-ramp and design new tracking controllers to implement the planned trajectories. PPENIX SIMPLE MOTION PLNNING METHO This paper uses a similar motion planning method as used in [14]. The method can be easily derived by basic kinematics and requires little computational cost. ccelerating to a cruising velocity, then operating at the cruising velocity vcru t1 tassign Keeping accelerating. t1=tassign a = a max t 1 = t assign t 1 v cru = v 0 + a t 1 a = 2x 0 2v 0 t assign t 2 assign t 1 = t assign v cru = v 0 + a t 1 ecelerating to a cruising velocity, then operating at the cruising velocity vcru t1 tassign Keeping decelerating t1=tassign Keeping a constant velocity tassign 1 t = (a tassign ) 2 +2a(v 0 t assign x 0 ) a REFERENES a = a min t 1 = t assign + t 1 v cru = v 0 + a t 1 a = 2x 0 2v 0 t assign t 2 assign t 1 = t assign v cru = v 0 + a t 1 a = 0 t 1 = 0 v cru = v 0 v 0 t assign = x 0 [1]. Schrank,. Eisele, T. Lomax, and J. ak, 2015 urban mobility scorecard, Texas &M Transp. Inst., ollege Station, TX, US, [2] V. L. Knoop, H. J. Zuylen, and S. P. 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